Any reliance of either type of architecture on deterministic sources of optical GKP qubits is at odds with the current state of theory and technology.
The numerous procedures for generating optical GKP states that have been proposed tend either to be non-deterministic, as they rely on post-selected measurements directly [1]}, [2]}, [3]}, [4]}, [5]}, [6]} or indirectly [7]}, [8]}, [9]}; or require the experimentally challenging conditions of coherent interactions with matter [10]}, [11]} or extremely strong optical nonlinearity [11]}.
Recent advances in photon-number-resolving (PNR) detectors [13]}, [14]}, [15]}, [16]} have substantially improved the viability of the post-selection approach in the near term, with methods based on Gaussian boson sampling (GBS) [3]}, [4]}, [5]}, [6]} now within reach of state-of-the-art optical devices.
Low-probability sources can be improved with the help of multiplexing at the cost of an increased overhead.
That is, in order to generate states with near-unit probability \(1-p_{0}\) , the number of required state generation devices scales as \(\log (1/p_{0})\) , which is prohibitively large as \(p_{0} \rightarrow 0\) .
